1 Script Overview

Built with R 3.6.2

This script runs analyses on data from the SPECTRE study. Specifically, it investigates different read-outs as a function of whether participants experienced controllable or uncontrollable stress (or no stress). Measurements under investigation comprised participant ratings (stressor aversiveness, perceived control, stress, helplessness), reaction times, correct responses, and heart rates. In addition, MR parameter estimates from a GLM analysis of related imaging data were investigated and linked to the ratings.

Here we use the following abbreviations: controllable stress = con; uncontrollable stress = noc, baseline = bas.

Linear mixed-effects models were constructed based on the tutorial referenced in Singmann & Kellen, 2019: https://cran.r-project.org/web/packages/afex/vignettes/afex_mixed_example.html

2 Sample Descriptives

N = 45 participants aged 19-30 took part in this study (46.67 % female, age: M = 25, SD = 3.05).

3 Manipulation Checks

3.1 Version Counterbalancing

## 
## 1 2 3 4 5 6 
## 8 8 8 8 6 7

3.2 Yoking of Stress Durations

## 
##  Paired t-test
## 
## data:  stressDur$total_con_stress_dur and stressDur$total_noc_stress_dur
## t = 6.3263, df = 44, p-value = 1.117e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.178446 2.280295
## sample estimates:
## mean of the differences 
##                 1.72937
## 
## Cohen's d
## 
## d estimate: 1.004407 (large)
## 95 percent confidence interval:
##    lower    upper 
## 0.559817 1.448996
## [1] 1.833766

There was a significant difference in overall stress duration between conditions, yoking did not work out properly. Participants were on average exposed to LESS stress in the uncontrollable condition but reported experiencing no difference or even MORE stress in this condition when asked afterwards. Therefore, effects showing greater performance decrements associated with uncontrollable stress cannot be attributed to more stress. Nevertheless, this remains a limitation and the CON-UNCON stress duration difference is therefore included as a covariate in subsequent analyses.

3.3 Stressor Aversiveness

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## aversiveness ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2512.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8204 -0.4590 -0.0135  0.5387  3.1386 
## 
## Random effects:
##  Groups   Name              Variance  Std.Dev. Corr                   
##  id       (Intercept)       2.123e+02 14.56928                        
##           condition1        9.658e-03  0.09827  0.24                  
##           run.z             4.903e+01  7.00240  0.45  0.97            
##           stress_dur_diff.z 3.962e+00  1.99037 -0.99 -0.36 -0.56      
##           condition1:run.z  1.192e-01  0.34524  0.42  0.98  1.00 -0.54
##  Residual                   3.107e+01  5.57371                        
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       64.2346     2.1160  33.6567  30.356  < 2e-16 ***
## condition1        -0.4302     0.2958 257.4147  -1.455  0.14702    
## run.z             -3.6294     1.0812  44.4496  -3.357  0.00162 ** 
## condition1:run.z  -0.2053     0.3002 204.2381  -0.684  0.49488    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.011              
## run.z       0.415  0.047       
## cndtn1:rn.z 0.069  0.008  0.164
## convergence code: 1
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + re1.condition1 + re1.run.z +  
##     re1.stress_dur_diff.z + re1.condition1_by_run.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2523
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9451 -0.4570 -0.0275  0.5309  3.1533 
## 
## Random effects:
##  Groups   Name                    Variance Std.Dev.
##  id       (Intercept)             210.14   14.496  
##  id.1     re1.condition1            0.00    0.000  
##  id.2     re1.run.z                49.07    7.005  
##  id.3     re1.stress_dur_diff.z     0.00    0.000  
##  id.4     re1.condition1_by_run.z   0.00    0.000  
##  Residual                          31.25    5.590  
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8372     2.1816  43.8455  29.261  < 2e-16 ***
## condition1        -0.4354     0.2963 264.1050  -1.470  0.14286    
## run.z             -3.7103     1.0871  44.1177  -3.413  0.00139 ** 
## condition1:run.z  -0.2151     0.2967 264.1050  -0.725  0.46901    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.001  0.000       
## cndtn1:rn.z 0.000  0.000  0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                    Std.Dev.
##  id       (Intercept)             14.4963 
##  id.1     re1.condition1           0.0000 
##  id.2     re1.run.z                7.0047 
##  id.3     re1.stress_dur_diff.z    0.0000 
##  id.4     re1.condition1_by_run.z  0.0000 
##  Residual                          5.5899
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + re1.condition1 + re1.run.z +  
##     re1.stress_dur_diff.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2523
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9451 -0.4570 -0.0275  0.5309  3.1533 
## 
## Random effects:
##  Groups   Name                  Variance  Std.Dev. 
##  id       (Intercept)           2.101e+02 1.450e+01
##  id.1     re1.condition1        0.000e+00 0.000e+00
##  id.2     re1.run.z             4.907e+01 7.005e+00
##  id.3     re1.stress_dur_diff.z 3.523e-13 5.936e-07
##  Residual                       3.125e+01 5.590e+00
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8372     2.1816  43.8455  29.261  < 2e-16 ***
## condition1        -0.4354     0.2963 264.1050  -1.470  0.14286    
## run.z             -3.7103     1.0871  44.1177  -3.413  0.00139 ** 
## condition1:run.z  -0.2151     0.2967 264.1050  -0.725  0.46901    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.001  0.000       
## cndtn1:rn.z 0.000  0.000  0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                  Std.Dev.  
##  id       (Intercept)           1.4496e+01
##  id.1     re1.condition1        0.0000e+00
##  id.2     re1.run.z             7.0047e+00
##  id.3     re1.stress_dur_diff.z 5.9355e-07
##  Residual                       5.5899e+00
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + run.z + stress_dur_diff.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2523
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9451 -0.4570 -0.0275  0.5309  3.1533 
## 
## Random effects:
##  Groups   Name              Variance  Std.Dev. 
##  id       (Intercept)       2.101e+02 1.450e+01
##  id.1     run.z             4.907e+01 7.005e+00
##  id.2     stress_dur_diff.z 7.766e-15 8.813e-08
##  Residual                   3.125e+01 5.590e+00
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8372     2.1816  43.8455  29.261  < 2e-16 ***
## condition1        -0.4354     0.2963 264.1050  -1.470  0.14286    
## run.z             -3.7103     1.0871  44.1177  -3.413  0.00139 ** 
## condition1:run.z  -0.2151     0.2967 264.1050  -0.725  0.46901    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.001  0.000       
## cndtn1:rn.z 0.000  0.000  0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2515.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9268 -0.4541 -0.0162  0.5456  3.1957 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  id       (Intercept) 211.18   14.532       
##           run.z        49.01    7.001   0.42
##  Residual              31.24    5.590       
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8377     2.1869  43.8362  29.191  < 2e-16 ***
## condition1        -0.4354     0.2962 264.1496  -1.470  0.14284    
## run.z             -3.7096     1.0865  44.1244  -3.414  0.00138 ** 
## condition1:run.z  -0.2151     0.2967 264.1496  -0.725  0.46899    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.398  0.000       
## cndtn1:rn.z 0.000  0.000  0.000

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## avers.m4c: aversiveness ~ condition * run.z + (1 + run.z | id)
## avers.maxc: aversiveness ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z | 
## avers.maxc:     id)
##            Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
## avers.m4c   8 2535.5 2566.5 -1259.8   2519.5                         
## avers.maxc 20 2556.3 2633.8 -1258.2   2516.3 3.1834     12     0.9941
  Fixed Effects - Stressor Aversiveness
Predictors Estimates 95% CI p
Intercept 63.84 59.55 – 68.12 <0.001
Condition -0.44 -1.02 – 0.15 0.143
Run -3.71 -5.84 – -1.58 0.001
Condition x Run -0.22 -0.80 – 0.37 0.469
Random Effects
σ2 31.24
τ00 id 211.18
τ11 id.run.z 49.01
ρ01 id 0.42
ICC 0.89
N id 45
Marginal R2 / Conditional R2 0.046 / 0.898

Participants rated the stressor as very aversive in both controllable and uncontrollable trials (global M = 63.75). In both conditions, aversiveness ratings decreased slightly over runs.

3.4 Perceived Control

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## control ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3030.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2040 -0.4675  0.0540  0.4761  3.0614 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr                   
##  id       (Intercept)         6.161   2.482                          
##           condition1         95.580   9.776   -0.50                  
##           run.z              35.038   5.919   -0.22 -0.03            
##           stress_dur_diff.z 187.870  13.707   -0.79 -0.09  0.05      
##           condition1:run.z   14.140   3.760   -0.29  0.59 -0.29 -0.06
##  Residual                   163.912  12.803                          
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)       46.6964     1.3223 71.6054  35.315  < 2e-16 ***
## condition1        16.4062     1.6051 44.1879  10.221 3.23e-13 ***
## run.z              0.8908     1.1165 40.3465   0.798   0.4297    
## condition1:run.z   1.7884     0.8843 44.3610   2.023   0.0492 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z 
## condition1  -0.123              
## run.z       -0.044 -0.021       
## cndtn1:rn.z -0.051  0.342 -0.147
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## control ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3039
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3188 -0.4210  0.0349  0.5060  3.0524 
## 
## Random effects:
##  Groups   Name               Variance Std.Dev. Corr 
##  id       (Intercept)          0.2108  0.4592       
##  id.1     conditioncon        89.4320  9.4568       
##           conditionnoc       126.5411 11.2490  -0.79
##  id.2     run.z               22.8396  4.7791       
##  id.3     stress_dur_diff.z  190.2152 13.7919       
##  id.4     conditioncon:run.z  13.1683  3.6288       
##           conditionnoc:run.z  39.9533  6.3209  -0.07
##  Residual                    164.6075 12.8299       
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)       46.6816     1.3809 14.6523  33.806 2.58e-15 ***
## condition1        16.4389     1.6108 44.2287  10.206 3.34e-13 ***
## run.z              0.8883     1.1207 40.4252   0.793   0.4326    
## condition1:run.z   1.7870     0.8845 44.4677   2.020   0.0494 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z 
## condition1  -0.093              
## run.z        0.008  0.000       
## cndtn1:rn.z -0.001  0.003 -0.151
## convergence code: 0
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?
##  Groups   Name               Std.Dev. Corr  
##  id       (Intercept)         0.45917       
##  id.1     conditioncon        9.45685       
##           conditionnoc       11.24905 -0.786
##  id.2     run.z               4.77908       
##  id.3     stress_dur_diff.z  13.79185       
##  id.4     conditioncon:run.z  3.62882       
##           conditionnoc:run.z  6.32086 -0.069
##  Residual                    12.82995
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## control ~ condition * run.z + (1 + condition + run.z + stress_dur_diff.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3045.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2505 -0.4610  0.0405  0.4961  3.6482 
## 
## Random effects:
##  Groups   Name              Variance  Std.Dev.  Corr 
##  id       (Intercept)       1.283e-09 3.582e-05      
##  id.1     conditioncon      8.433e+01 9.183e+00      
##           conditionnoc      1.216e+02 1.103e+01 -0.83
##  id.2     run.z             3.223e+01 5.678e+00      
##  id.3     stress_dur_diff.z 1.904e+02 1.380e+01      
##  Residual                   1.868e+02 1.367e+01      
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       46.6663     1.3827  14.5964  33.750 2.91e-15 ***
## condition1        16.4454     1.6122  44.2038  10.200 3.42e-13 ***
## run.z              0.8747     1.1179  40.3191   0.782   0.4385    
## condition1:run.z   1.7959     0.7272 218.9354   2.470   0.0143 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z 
## condition1  -0.093              
## run.z        0.008  0.000       
## cndtn1:rn.z  0.000  0.002  0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name              Std.Dev.   Corr  
##  id       (Intercept)       3.5817e-05       
##  id.1     conditioncon      9.1833e+00       
##           conditionnoc      1.1028e+01 -0.825
##  id.2     run.z             5.6775e+00       
##  id.3     stress_dur_diff.z 1.3797e+01       
##  Residual                   1.3668e+01
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: control ~ condition * run.z + (1 + condition + run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3051.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3566 -0.4820  0.0051  0.4759  3.5258 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr       
##  id       (Intercept) 128.08   11.317              
##           condition1   93.24    9.656   -0.06      
##           run.z        31.99    5.656    0.27 -0.04
##  Residual             187.17   13.681              
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       48.2104     1.8378  44.2242  26.233  < 2e-16 ***
## condition1        16.4441     1.6122  44.2044  10.200 3.43e-13 ***
## run.z              0.8685     1.1173  39.6417   0.777   0.4416    
## condition1:run.z   1.7941     0.7279 217.7533   2.465   0.0145 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z 
## condition1  -0.050              
## run.z        0.190 -0.024       
## cndtn1:rn.z  0.000  0.002  0.000

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## ctrl.m3c: control ~ condition * run.z + (1 + condition + run.z | id)
## ctrl.maxc: control ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z | 
## ctrl.maxc:     id)
##           Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)  
## ctrl.m3c  11 3082.6 3125.2 -1530.3   3060.6                           
## ctrl.maxc 20 3079.4 3156.9 -1519.7   3039.4 21.253      9    0.01157 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  Fixed Effects - Perceived Control
Predictors Estimates 95% CI p
Intercept 48.21 44.61 – 51.81 <0.001
Condition 16.44 13.28 – 19.60 <0.001
Run 0.87 -1.32 – 3.06 0.442
Condition x Run 1.79 0.37 – 3.22 0.014
Random Effects
σ2 187.17
τ00 id 128.08
τ11 id.condition1 93.24
τ11 id.run.z 31.99
ρ01 -0.06
0.27
ICC 0.57
N id 45
Marginal R2 / Conditional R2 0.385 / 0.738

Participants reported higher perceived control under controllable trials compared to uncontrollable trials. Ratings increased over runs for controllable stress, but decreased for uncontrollable stress.

4 Ratings

4.1 Stress

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition * run.z + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4260.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.9213 -0.4045 -0.0382  0.3733  4.3181 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr                         
##  id       (Intercept)       255.815  15.994                                
##           condition1        179.777  13.408   -0.26                        
##           condition2         65.848   8.115    0.22 -0.78                  
##           run.z              24.979   4.998    0.15  0.13  0.01            
##           stress_dur_diff.z  33.751   5.810    0.54 -0.72  0.26 -0.42      
##           condition1:run.z    7.812   2.795   -0.51  0.05 -0.11 -0.92  0.10
##           condition2:run.z    2.466   1.570    0.20 -0.02  0.58  0.55 -0.48
##  Residual                    81.139   9.008                                
##       
##       
##       
##       
##       
##       
##       
##  -0.52
##       
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   39.904      2.206  36.262  18.093  < 2e-16 ***
## condition1   -17.610      2.005  41.349  -8.783 5.33e-11 ***
## condition2     7.414      1.294  44.055   5.729 8.39e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.196       
## condition2  0.185 -0.766
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## stress ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +  
##     re1.stress_dur_diff.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4323.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4502 -0.3849 -0.0329  0.3338  4.0466 
## 
## Random effects:
##  Groups   Name                    Variance Std.Dev.
##  id       (Intercept)             266.691  16.331  
##  id.1     re1.condition1          162.838  12.761  
##  id.2     re1.condition2           58.278   7.634  
##  id.3     re1.run.z                24.409   4.941  
##  id.4     re1.stress_dur_diff.z     0.000   0.000  
##  id.5     re1.condition1_by_run.z   5.207   2.282  
##  id.6     re1.condition2_by_run.z   0.000   0.000  
##  Residual                          85.267   9.234  
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   36.930      2.468  44.014  14.967  < 2e-16 ***
## condition1   -18.246      1.985  43.951  -9.193 8.48e-12 ***
## condition2     7.110      1.271  44.057   5.595 1.32e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.063
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                    Std.Dev.
##  id       (Intercept)             16.3307 
##  id.1     re1.condition1          12.7608 
##  id.2     re1.condition2           7.6340 
##  id.3     re1.run.z                4.9406 
##  id.4     re1.stress_dur_diff.z    0.0000 
##  id.5     re1.condition1_by_run.z  2.2820 
##  id.6     re1.condition2_by_run.z  0.0000 
##  Residual                          9.2340
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition + run.z + stress_dur_diff.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4292.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.5256 -0.3841 -0.0554  0.3751  4.1937 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr       
##  id       (Intercept)       193.85   13.923              
##  id.1     conditionbas      146.03   12.084              
##           conditioncon      189.47   13.765   -0.24      
##           conditionnoc      200.17   14.148   -0.28  0.75
##  id.2     run.z              23.96    4.895              
##  id.3     stress_dur_diff.z   0.00    0.000              
##  Residual                    89.42    9.456              
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   36.931      2.468  44.014  14.962  < 2e-16 ***
## condition1   -18.223      2.079  44.003  -8.766 3.30e-11 ***
## condition2     7.121      1.330  44.098   5.352 2.97e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.229       
## condition2  0.177 -0.744
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name              Std.Dev. Corr         
##  id       (Intercept)       13.923                
##  id.1     conditionbas      12.084                
##           conditioncon      13.765   -0.236       
##           conditionnoc      14.148   -0.280  0.750
##  id.2     run.z              4.895                
##  id.3     stress_dur_diff.z  0.000                
##  Residual                    9.456
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition + run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4290.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.5270 -0.3883 -0.0462  0.3709  4.1945 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr             
##  id       (Intercept) 267.24   16.347                    
##           condition1  180.09   13.420   -0.24            
##           condition2   64.51    8.032    0.20 -0.79      
##           run.z        23.98    4.897    0.14  0.15 -0.01
##  Residual              89.41    9.456                    
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   37.888      2.453  43.999  15.443  < 2e-16 ***
## condition1   -17.387      2.067  44.034  -8.412 1.04e-10 ***
## condition2     7.098      1.330  44.102   5.336 3.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.244       
## condition2  0.178 -0.748

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## stress.m3c: stress ~ condition + (1 + condition + run.z | id)
## stress.maxc: stress ~ condition + (1 + condition * run.z + stress_dur_diff.z | 
## stress.maxc:     id)
##             Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)  
## stress.m3c  14 4327.4 4387.3 -2149.7   4299.4                           
## stress.maxc 32 4332.5 4469.5 -2134.2   4268.5 30.873     18    0.02977 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##  condition emmean   SE df lower.CL upper.CL
##  bas         20.5 2.86 44     14.7     26.3
##  con         45.0 3.06 44     38.8     51.2
##  noc         48.2 3.11 44     41.9     54.4
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95
##  contrast  estimate   SE df t.ratio p.value
##  bas - con   -24.48 3.26 44 -7.515  <.0001 
##  bas - noc   -27.68 3.33 44 -8.300  <.0001 
##  con - noc    -3.19 1.81 44 -1.765  0.0845 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Stress
Predictors Estimates 95% CI p
Intercept 37.89 33.08 – 42.70 <0.001
Condition-CON -17.39 -21.44 – -13.34 <0.001
Condition-UNCON 7.10 4.49 – 9.70 <0.001
Random Effects
σ2 89.41
τ00 id 267.24
τ11 id.condition1 180.09
τ11 id.condition2 64.51
τ11 id.run.z 23.98
ρ01 -0.24
0.20
0.14
ICC 0.81
N id 45
Marginal R2 / Conditional R2 0.249 / 0.855
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## stress ~ condition * aversiveness.z + (1 + condition * aversiveness.z +  
##     run.z | id) + (1 | run)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2869.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9148 -0.3764 -0.0081  0.3585  3.8930 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr                   
##  id       (Intercept)               292.120  17.092                          
##           condition1                 13.650   3.695   -0.12                  
##           aversiveness.z             46.175   6.795   -0.31 -0.64            
##           run.z                      20.166   4.491   -0.18  0.31  0.44      
##           condition1:aversiveness.z   8.834   2.972    0.48  0.70 -0.95 -0.28
##  run      (Intercept)                 0.000   0.000                          
##  Residual                           101.356  10.068                          
## Number of obs: 356, groups:  id, 45; run, 4
## 
## Fixed effects:
##                           Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)                46.7521     2.6390 41.1145  17.716  < 2e-16 ***
## condition1                 -2.3315     0.7898 42.4631  -2.952  0.00513 ** 
## aversiveness.z              4.9076     1.5789 23.0594   3.108  0.00494 ** 
## condition1:aversiveness.z   1.0953     0.7849 36.2080   1.395  0.17138    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 avrsv.
## condition1  -0.112              
## aversvnss.z -0.179 -0.255       
## cndtn1:vrs.  0.222  0.335 -0.467
## convergence code: 0
## boundary (singular) fit: see ?isSingular

Participants reported higher stress levels in both stress conditions compared to baseline. There was no difference in stress ratings between controllable and uncontrollable stress trials.

4.2 Helplessness

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## helplessness ~ condition + (1 + condition * run.z + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3098.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.94407 -0.42820 -0.03208  0.38843  2.75336 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr                   
##  id       (Intercept)       240.026  15.493                          
##           condition1        138.447  11.766   -0.09                  
##           run.z              36.607   6.050   -0.03 -0.13            
##           stress_dur_diff.z  88.438   9.404    0.13  0.51 -0.22      
##           condition1:run.z    8.119   2.849   -0.22  0.46  0.03  0.46
##  Residual                   172.909  13.149                          
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   45.781      2.556  32.288  17.909  < 2e-16 ***
## condition1   -10.502      1.800  40.648  -5.833 7.68e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr)
## condition1 -0.101

## $id
  Fixed Effects - Helplessness
Predictors Estimates 95% CI p
Intercept 45.78 40.77 – 50.79 <0.001
Condition -10.50 -14.03 – -6.97 <0.001
Random Effects
σ2 172.91
τ00 id 240.03
τ11 id.condition1 138.45
τ11 id.run.z 36.61
τ11 id.stress_dur_diff.z 88.44
τ11 id.condition1:run.z 8.12
ρ01 -0.09
-0.03
0.13
-0.22
ICC 0.69
N id 45
Marginal R2 / Conditional R2 0.167 / 0.739

Participants reported feeling less helpless in controllable trials compared to uncontrollable trials.

5 Reaction Times (RT)

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + condition * run.z + stress_dur_diff.z |      id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58659.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1193 -0.6576 -0.0151  0.6336  3.3257 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr                         
##  id       (Intercept)         989.67  31.459                               
##           condition1          309.79  17.601  -0.46                        
##           condition2           71.98   8.484   0.44 -0.99                  
##           run.z                71.19   8.437   0.45  0.16 -0.24            
##           stress_dur_diff.z  1509.89  38.857   0.06  0.36 -0.32 -0.16      
##           condition1:run.z    131.62  11.473   0.08 -0.23  0.23 -0.33  0.72
##           condition2:run.z     50.44   7.102  -0.08 -0.02 -0.07  0.65 -0.69
##  Residual                   10574.83 102.834                               
##       
##       
##       
##       
##       
##       
##       
##  -0.46
##       
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  768.500      5.759  36.296 133.449  < 2e-16 ***
## condition1    17.527      3.532  41.791   4.962 1.22e-05 ***
## condition2   -26.592      2.389  68.600 -11.129  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.302       
## condition2  0.205 -0.724
## convergence code: 1
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +  
##     re1.stress_dur_diff.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58685.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0492 -0.6560 -0.0204  0.6269  3.3666 
## 
## Random effects:
##  Groups   Name                    Variance Std.Dev.
##  id       (Intercept)              1072.77  32.753 
##  id.1     re1.condition1            120.43  10.974 
##  id.2     re1.condition2              0.00   0.000 
##  id.3     re1.run.z                  84.43   9.188 
##  id.4     re1.stress_dur_diff.z    1317.37  36.296 
##  id.5     re1.condition1_by_run.z   103.03  10.151 
##  id.6     re1.condition2_by_run.z    17.63   4.199 
##  Residual                         10632.30 103.113 
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  768.446      6.369   39.072 120.654  < 2e-16 ***
## condition1    18.784      3.029   77.844   6.202  2.5e-08 ***
## condition2   -27.105      2.078 4675.124 -13.043  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.073       
## condition2 -0.055 -0.511
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +  
##     re1.stress_dur_diff.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58691.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0612 -0.6505 -0.0200  0.6333  3.2452 
## 
## Random effects:
##  Groups   Name                  Variance  Std.Dev. 
##  id       (Intercept)           1.072e+03 3.275e+01
##  id.1     re1.condition1        1.195e+02 1.093e+01
##  id.2     re1.condition2        1.209e-11 3.478e-06
##  id.3     re1.run.z             8.913e+01 9.441e+00
##  id.4     re1.stress_dur_diff.z 1.313e+03 3.624e+01
##  Residual                       1.070e+04 1.035e+02
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  768.417      6.367   39.075 120.686  < 2e-16 ***
## condition1    18.732      3.028   78.092   6.186 2.64e-08 ***
## condition2   -27.090      2.084 4708.688 -13.002  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.073       
## condition2 -0.055 -0.512
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                  Std.Dev.  
##  id       (Intercept)           3.2747e+01
##  id.1     re1.condition1        1.0931e+01
##  id.2     re1.condition2        3.4776e-06
##  id.3     re1.run.z             9.4409e+00
##  id.4     re1.stress_dur_diff.z 3.6237e+01
##  Residual                       1.0346e+02
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + run.z + stress_dur_diff.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58695.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.05636 -0.65107 -0.01586  0.64175  3.15451 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr       
##  id       (Intercept)        1038.02  32.218             
##           run.z                84.66   9.201   0.37      
##           stress_dur_diff.z  1502.20  38.758  -0.02 -0.36
##  Residual                   10767.54 103.767             
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  769.377      6.172   38.024 124.653  < 2e-16 ***
## condition1    18.648      2.552 4745.939   7.306 3.21e-13 ***
## condition2   -27.038      2.089 4742.534 -12.943  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.089       
## condition2 -0.055 -0.609

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## rt.m3c: rt ~ condition + (1 + run.z + stress_dur_diff.z | id)
## rt.maxc: rt ~ condition + (1 + condition * run.z + stress_dur_diff.z | 
## rt.maxc:     id)
##         Df   AIC   BIC logLik deviance  Chisq Chi Df Pr(>Chisq)  
## rt.m3c  10 58727 58792 -29354    58707                           
## rt.maxc 32 58736 58944 -29336    58672 34.809     22    0.04056 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##  condition emmean   SE  df asymp.LCL asymp.UCL
##  bas          788 6.89 Inf       775       802
##  con          742 6.41 Inf       730       755
##  noc          778 6.41 Inf       765       790
## 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95
##  contrast  estimate   SE  df z.ratio p.value
##  bas - con     45.7 4.17 Inf  10.962 <.0001 
##  bas - noc     10.3 4.18 Inf   2.456 0.0140 
##  con - noc    -35.4 3.31 Inf -10.688 <.0001 
## 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Reaction Times
Predictors Estimates 95% CI p
Intercept 769.38 757.28 – 781.47 <0.001
Condition-CON 18.65 13.65 – 23.65 <0.001
Condition-UNCON -27.04 -31.13 – -22.94 <0.001
Random Effects
σ2 10767.54
τ00 id 1038.02
τ11 id.run.z 84.66
τ11 id.stress_dur_diff.z 1502.20
ρ01 0.37
-0.02
ICC 0.09
N id 45
Marginal R2 / Conditional R2 0.031 / 0.116

Reaction times were shorter under stress compared to baseline. Further, participants responded faster in the controllable condition compared to the uncontrollable condition.

6 Correct Responses

## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + condition * run.z + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3639.8   3842.4  -1788.9   3577.8     5068 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -7.0043  0.2166  0.3055  0.3808  0.9227 
## 
## Random effects:
##  Groups Name              Variance Std.Dev. Corr                               
##  id     (Intercept)       0.13826  0.3718                                      
##         condition1        0.06058  0.2461   -0.28                              
##         condition2        0.06208  0.2492   -0.42 -0.75                        
##         run.z             0.10555  0.3249    0.62 -0.91  0.43                  
##         stress_dur_diff.z 0.43368  0.6585   -0.58  0.94 -0.49 -0.97            
##         condition1:run.z  0.06074  0.2464   -0.07  0.90 -0.79 -0.81  0.74      
##         condition2:run.z  0.09416  0.3069    0.06 -0.85  0.76  0.63 -0.79 -0.60
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.9245     0.1617  11.902   <2e-16 ***
## condition1   -0.2031     0.1259  -1.614   0.1066    
## condition2    0.2300     0.1219   1.887   0.0591 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.045       
## condition2 -0.316 -0.528
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + re1.condition1 + re1.condition2 +  
##     re1.run.z + re1.stress_dur_diff.z + re1.condition1_by_run.z +  
##     re1.condition2_by_run.z || id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3632.1   3697.5  -1806.1   3612.1     5089 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.2326  0.2325  0.3034  0.3907  0.9230 
## 
## Random effects:
##  Groups Name                    Variance  Std.Dev.
##  id     (Intercept)             0.1712604 0.41384 
##  id.1   re1.condition1          0.0003078 0.01754 
##  id.2   re1.condition2          0.0000000 0.00000 
##  id.3   re1.run.z               0.0584192 0.24170 
##  id.4   re1.stress_dur_diff.z   0.3524759 0.59370 
##  id.5   re1.condition1_by_run.z 0.0157318 0.12543 
##  id.6   re1.condition2_by_run.z 0.0493952 0.22225 
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.08868    0.10831  19.285  < 2e-16 ***
## condition1  -0.32451    0.06750  -4.807 1.53e-06 ***
## condition2   0.30690    0.06335   4.844 1.27e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.057       
## condition2 -0.007 -0.574
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups Name                    Std.Dev.
##  id     (Intercept)             0.413836
##  id.1   re1.condition1          0.017545
##  id.2   re1.condition2          0.000000
##  id.3   re1.run.z               0.241701
##  id.4   re1.stress_dur_diff.z   0.593697
##  id.5   re1.condition1_by_run.z 0.125427
##  id.6   re1.condition2_by_run.z 0.222250
## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + condition + run.z + stress_dur_diff.z ||  
##     id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3636.3   3714.7  -1806.1   3612.3     5087 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.7146  0.2333  0.3053  0.3847  0.9688 
## 
## Random effects:
##  Groups Name              Variance  Std.Dev.  Corr     
##  id     (Intercept)       1.683e-13 4.102e-07          
##  id.1   conditionbas      1.181e-01 3.437e-01          
##         conditioncon      4.848e-02 2.202e-01 1.00     
##         conditionnoc      2.516e-01 5.016e-01 1.00 1.00
##  id.2   run.z             5.914e-02 2.432e-01          
##  id.3   stress_dur_diff.z 4.324e-01 6.576e-01          
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.04907    0.10341  19.815  < 2e-16 ***
## condition1  -0.31784    0.06989  -4.548 5.42e-06 ***
## condition2   0.27516    0.06694   4.110 3.95e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.072       
## condition2 -0.203 -0.521
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups Name              Std.Dev.   Corr       
##  id     (Intercept)       4.1019e-07            
##  id.1   conditionbas      3.4368e-01            
##         conditioncon      2.2018e-01 1.000      
##         conditionnoc      5.0159e-01 1.000 1.000
##  id.2   run.z             2.4320e-01            
##  id.3   stress_dur_diff.z 6.5756e-01
## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + condition + stress_dur_diff.z || id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3642.1   3714.0  -1810.1   3620.1     5088 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.6926  0.2298  0.3099  0.3859  0.8294 
## 
## Random effects:
##  Groups Name              Variance  Std.Dev.  Corr     
##  id     (Intercept)       8.694e-14 2.949e-07          
##  id.1   conditionbas      1.129e-01 3.360e-01          
##         conditioncon      4.718e-02 2.172e-01 1.00     
##         conditionnoc      2.465e-01 4.965e-01 1.00 1.00
##  id.2   stress_dur_diff.z 4.384e-01 6.621e-01          
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.02673    0.10241  19.789  < 2e-16 ***
## condition1  -0.31598    0.06982  -4.525 6.03e-06 ***
## condition2   0.27365    0.06680   4.096 4.20e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.069       
## condition2 -0.201 -0.519
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + stress_dur_diff.z || id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3634.5   3667.1  -1812.2   3624.5     5094 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.3455  0.2389  0.3074  0.3936  0.8272 
## 
## Random effects:
##  Groups Name              Variance Std.Dev.
##  id     (Intercept)       0.1672   0.4089  
##  id.1   stress_dur_diff.z 0.3577   0.5981  
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.05032    0.10725  19.117  < 2e-16 ***
## condition1  -0.30968    0.06692  -4.628 3.69e-06 ***
## condition2   0.30177    0.06209   4.860 1.17e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.067       
## condition2 -0.007 -0.582

## $id

## Fitting 2 (g)lmer() models:
## [..]
## Fitting 2 (g)lmer() models:
## [..]
## Data: data
## Models:
## corr.m4c: correct ~ condition + (1 + stress_dur_diff.z || id)
## corr.maxc: correct ~ condition + (1 + condition * run.z + stress_dur_diff.z | 
## corr.maxc:     id)
##           Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)   
## corr.m4c   5 3634.5 3667.1 -1812.2   3624.5                            
## corr.maxc 31 3639.8 3842.4 -1788.9   3577.8 46.687     26   0.007636 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##  condition emmean    SE  df asymp.LCL asymp.UCL
##  bas         1.74 0.130 Inf      1.49      2.00
##  con         2.35 0.124 Inf      2.11      2.59
##  noc         2.06 0.119 Inf      1.83      2.29
## 
## Results are given on the logit (not the response) scale. 
## Confidence level used: 0.95
##  contrast  estimate    SE  df z.ratio p.value
##  bas - con   -0.611 0.115 Inf -5.329  <.0001 
##  bas - noc   -0.318 0.110 Inf -2.887  0.0073 
##  con - noc    0.294 0.101 Inf  2.905  0.0073 
## 
## Results are given on the log odds ratio (not the response) scale. 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Correct Responses
Predictors Estimates 95% CI p
Intercept 2.05 1.84 – 2.26 <0.001
Condition-CON -0.31 -0.44 – -0.18 <0.001
Condition-UNCON 0.30 0.18 – 0.42 <0.001
Random Effects
σ2 3.29
τ00 id 0.17
τ00 id.1 0.36
ICC 0.05
N id 44
Marginal R2 / Conditional R2 0.015 / 0.062

Performance was significantly better (higher rate of correct responses) under stress compared to baseline. Further, participants responded correctly more often in the controllable condition compared to the uncontrollable condition.

7 Heart Rate (HR)

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + condition * run.z + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2469.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8383 -0.4901 -0.0126  0.4777  6.6188 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr                         
##  id       (Intercept)       128.5617 11.3385                               
##           condition1          0.1935  0.4399  -0.11                        
##           condition2          0.1867  0.4321   0.41 -0.95                  
##           run.z               8.3145  2.8835  -0.47  0.93 -1.00            
##           stress_dur_diff.z  12.1787  3.4898   0.80  0.11  0.14 -0.22      
##           condition1:run.z    0.1235  0.3514   0.83 -0.60  0.81 -0.86  0.67
##           condition2:run.z    0.4259  0.6526  -0.58  0.87 -0.98  0.99 -0.33
##  Residual                     5.9810  2.4456                               
##       
##       
##       
##       
##       
##       
##       
##  -0.91
##       
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  60.2838     1.4482  33.2819  41.627   <2e-16 ***
## condition1   -0.2322     0.1636 269.1272  -1.420    0.157    
## condition2    0.2107     0.1620 360.2372   1.301    0.194    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.127       
## condition2 -0.008 -0.504
## convergence code: 1
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +  
##     re1.stress_dur_diff.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2496.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5023 -0.4937 -0.0187  0.4300  6.5337 
## 
## Random effects:
##  Groups   Name                    Variance  Std.Dev. 
##  id       (Intercept)             1.058e+02 1.029e+01
##  id.1     re1.condition1          0.000e+00 0.000e+00
##  id.2     re1.condition2          0.000e+00 0.000e+00
##  id.3     re1.run.z               8.187e+00 2.861e+00
##  id.4     re1.stress_dur_diff.z   1.372e+01 3.704e+00
##  id.5     re1.condition1_by_run.z 0.000e+00 0.000e+00
##  id.6     re1.condition2_by_run.z 1.269e-14 1.126e-07
##  Residual                         6.353e+00 2.520e+00
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  64.4401     1.6708  40.7322  38.569  < 2e-16 ***
## condition1   -0.5347     0.1658 375.8336  -3.224  0.00137 ** 
## condition2    0.5405     0.1658 375.8336   3.259  0.00122 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.500
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                    Std.Dev.  
##  id       (Intercept)             1.0288e+01
##  id.1     re1.condition1          0.0000e+00
##  id.2     re1.condition2          0.0000e+00
##  id.3     re1.run.z               2.8612e+00
##  id.4     re1.stress_dur_diff.z   3.7036e+00
##  id.5     re1.condition1_by_run.z 0.0000e+00
##  id.6     re1.condition2_by_run.z 1.1263e-07
##  Residual                         2.5205e+00
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + re1.run.z + re1.stress_dur_diff.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2496.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5023 -0.4937 -0.0187  0.4300  6.5337 
## 
## Random effects:
##  Groups   Name                  Variance Std.Dev.
##  id       (Intercept)           105.846  10.288  
##  id.1     re1.run.z               8.187   2.861  
##  id.2     re1.stress_dur_diff.z  13.717   3.704  
##  Residual                         6.353   2.520  
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  64.4401     1.6708  40.7322  38.569  < 2e-16 ***
## condition1   -0.5347     0.1658 375.8336  -3.224  0.00137 ** 
## condition2    0.5405     0.1658 375.8336   3.259  0.00122 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.500

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## hr.m2c: bpm ~ condition + (1 + re1.run.z + re1.stress_dur_diff.z || id)
## hr.maxc: bpm ~ condition + (1 + condition * run.z + stress_dur_diff.z | 
## hr.maxc:     id)
##         Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
## hr.m2c   7 2509.2 2538.2 -1247.6   2495.2                         
## hr.maxc 32 2531.9 2664.2 -1233.9   2467.9 27.344     25     0.3389
##  condition emmean   SE   df lower.CL upper.CL
##  bas         63.9 1.73 41.1     60.4     67.4
##  con         65.0 1.73 41.1     61.5     68.5
##  noc         64.4 1.73 41.1     60.9     67.9
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95
##  contrast  estimate    SE  df t.ratio p.value
##  bas - con   -1.075 0.287 376 -3.743  0.0006 
##  bas - noc   -0.529 0.287 376 -1.841  0.1159 
##  con - noc    0.546 0.287 376  1.902  0.1159 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Heart Rate
Predictors Estimates 95% CI p
Intercept 64.44 61.17 – 67.71 <0.001
Condition-CON -0.53 -0.86 – -0.21 0.001
Condition-UNCON 0.54 0.22 – 0.87 0.001
Random Effects
σ2 6.35
τ00 id 105.85
τ00 id.1 8.19
τ00 id.2 13.72
ICC 0.94
N id 42
Marginal R2 / Conditional R2 0.002 / 0.943

Heart rates were higher under controllable stress compared to baseline. No other contrasts were significant.

8 MR Parameter Estimates from vmPFC

8.1 Does vmPFC activation modulate ratings?

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition * beta_weight.z + (1 + condition + run.z |      id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4028.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.6061 -0.4029 -0.0261  0.3556  4.1280 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr             
##  id       (Intercept) 263.82   16.243                    
##           condition1  180.09   13.420   -0.18            
##           condition2   69.25    8.322    0.16 -0.78      
##           run.z        21.82    4.671    0.32 -0.01  0.11
##  Residual              86.37    9.293                    
## Number of obs: 504, groups:  id, 42
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               39.3511     2.4500  41.3034  16.061  < 2e-16 ***
## condition1               -18.6571     2.1586  41.3842  -8.643 8.17e-11 ***
## condition2                 7.9990     1.4110  41.4656   5.669 1.23e-06 ***
## beta_weight.z             -0.1869     0.5870 402.5588  -0.319   0.7503    
## condition1:beta_weight.z   1.4957     0.7777 395.2965   1.923   0.0552 .  
## condition2:beta_weight.z  -0.4374     0.7754 395.7584  -0.564   0.5730    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 cndtn2 bt_wg. cn1:_.
## condition1  -0.174                            
## condition2   0.117 -0.732                     
## beta_wght.z  0.020 -0.057 -0.032              
## cndtn1:bt_. -0.066 -0.033  0.077 -0.141       
## cndtn2:bt_.  0.005  0.047 -0.017  0.100 -0.516
## $emtrends
##  condition beta_weight.z.trend    SE  df lower.CL upper.CL
##  bas                     1.309 0.915 383    -0.49    3.108
##  con                    -0.624 1.035 403    -2.66    1.410
##  noc                    -1.245 1.001 403    -3.21    0.722
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast  estimate   SE  df t.ratio p.value
##  bas - con    1.933 1.37 401 1.411   0.3361 
##  bas - noc    2.554 1.35 406 1.890   0.1429 
##  con - noc    0.621 1.36 380 0.458   0.8910 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + condition * run.z +  
##     stress_dur_diff.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2913.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.92054 -0.42509 -0.04567  0.39713  2.86551 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr                   
##  id       (Intercept)       270.736  16.454                          
##           condition1        135.044  11.621   -0.02                  
##           run.z              32.911   5.737    0.10 -0.28            
##           stress_dur_diff.z  39.069   6.250    0.08  0.97 -0.43      
##           condition1:run.z    7.487   2.736   -0.11  0.37  0.15  0.19
##  Residual                   174.622  13.214                          
## Number of obs: 336, groups:  id, 42
## 
## Fixed effects:
##                           Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)               46.05277    2.65442  40.92761  17.349  < 2e-16 ***
## condition1               -11.29240    1.80418  39.70543  -6.259  2.1e-07 ***
## beta_weight.z             -0.06404    1.05586 272.15763  -0.061   0.9517    
## condition1:beta_weight.z   2.01487    0.98620 241.14929   2.043   0.0421 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 bt_wg.
## condition1  -0.029              
## beta_wght.z  0.009 -0.138       
## cndtn1:bt_. -0.081  0.026  0.051
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name              Std.Dev. Corr                       
##  id       (Intercept)       16.4541                             
##           condition1        11.6208  -0.024                     
##           run.z              5.7368   0.097 -0.283              
##           stress_dur_diff.z  6.2505   0.078  0.972 -0.434       
##           condition1:run.z   2.7363  -0.110  0.366  0.149  0.190
##  Residual                   13.2145
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + condition + run.z +  
##     stress_dur_diff.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2916.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7040 -0.4376 -0.0566  0.4348  3.2418 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr             
##  id       (Intercept)       269.05   16.403                    
##           condition1        135.19   11.627   -0.02            
##           run.z              32.38    5.690    0.11 -0.32      
##           stress_dur_diff.z  44.05    6.637    0.08  0.96 -0.53
##  Residual                   186.07   13.641                    
## Number of obs: 336, groups:  id, 42
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               46.3897     2.6558  40.7747  17.467  < 2e-16 ***
## condition1               -11.8987     1.8302  40.1677  -6.501 9.17e-08 ***
## beta_weight.z              0.2606     1.0645 276.8869   0.245   0.8068    
## condition1:beta_weight.z   2.0794     0.9721 264.1351   2.139   0.0333 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 bt_wg.
## condition1  -0.036              
## beta_wght.z  0.014 -0.139       
## cndtn1:bt_. -0.070 -0.004  0.018
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## helplessness ~ condition * beta_weight.z + (1 + condition + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2932.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8579 -0.5138 -0.0332  0.4808  3.4685 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr       
##  id       (Intercept)       263.79   16.241              
##           condition1        128.66   11.343   -0.03      
##           stress_dur_diff.z  40.39    6.355    0.05  1.00
##  Residual                   227.53   15.084              
## Number of obs: 336, groups:  id, 42
## 
## Fixed effects:
##                          Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)                45.363      2.672  41.047  16.975  < 2e-16 ***
## condition1                -10.346      1.854  40.075  -5.580 1.83e-06 ***
## beta_weight.z              -1.298      1.059 279.951  -1.226    0.221    
## condition1:beta_weight.z    2.346      1.034 290.011   2.270    0.024 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 bt_wg.
## condition1  -0.053              
## beta_wght.z -0.005 -0.106       
## cndtn1:bt_. -0.070 -0.005  0.014
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + stress_dur_diff.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3007.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.88000 -0.52787 -0.00622  0.61977  2.43798 
## 
## Random effects:
##  Groups   Name              Variance Std.Dev. Corr 
##  id       (Intercept)       182.3    13.50         
##           stress_dur_diff.z 103.1    10.15    -0.15
##  Residual                   370.6    19.25         
## Number of obs: 336, groups:  id, 42
## 
## Fixed effects:
##                          Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)                46.611      2.677  37.022  17.413  < 2e-16 ***
## condition1                -10.004      1.078 293.217  -9.284  < 2e-16 ***
## beta_weight.z              -0.453      1.288 322.535  -0.352  0.72535    
## condition1:beta_weight.z    3.082      1.097 296.196   2.808  0.00531 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 bt_wg.
## condition1   0.000              
## beta_wght.z -0.001 -0.224       
## cndtn1:bt_. -0.074 -0.011  0.049
## $emtrends
##  condition beta_weight.z.trend   SE  df lower.CL upper.CL
##  con                      2.63 1.74 314   -0.802    6.060
##  noc                     -3.53 1.66 314   -6.803   -0.266
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast  estimate  SE  df t.ratio p.value
##  con - noc     6.16 2.2 296 2.805   0.0054 
## 
## Degrees-of-freedom method: kenward-roger
  Fixed Effects - Helplessness
Predictors Estimates 95% CI p
Intercept 46.61 41.36 – 51.86 <0.001
Condition -10.00 -12.12 – -7.89 <0.001
Beta Weight -0.45 -2.98 – 2.07 0.725
Condition x Beta Weight 3.08 0.93 – 5.23 0.005
Random Effects
σ2 370.61
τ00 id 182.35
τ11 id.stress_dur_diff.z 103.09
ρ01 id -0.15
ICC 0.33
N id 42
Marginal R2 / Conditional R2 0.168 / 0.442

VmPFC activation modulated helplessness ratings for uncontrollable stress, not for controllable stress. For uncontrollable stress, higher beta weights were linked to lower helplessness ratings.

9 Correction for Multiple Dependent Variables

##             DV p.orig Bonferroni
## 2 helplessness 0.0001     0.0005
## 3           RT 0.0001     0.0005
## 4      correct 0.0073     0.0365
## 1       stress 0.0845     0.4225
## 5           hr 0.1159     0.5795

10 Figures for Paper